### Browsing by Author "Gerek, Ö. N."

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Item Open Access A 2-D orientation-adaptive prediction filter in lifting structures for image coding(Institute of Electrical and Electronics Engineers, 2006) Gerek, Ö. N.; Çetin, A. EnisShow more Lifting-style implementations of wavelets are widely used in image coders. A two-dimensional (2-D) edge adaptive lifting structure, which is similar to Daubechies 5/3 wavelet, is presented. The 2-D prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image. Consequently, the prediction domain is allowed to rotate ±45° in regions with diagonal gradient. The gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction, and no multiplications are required.Show more Item Open Access Adaptive polyphase subband decomposition structures for image compression(IEEE, 2000) Gerek, Ö. N.; Çetin, A. EnisShow more Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented.Show more Item Open Access Block wavelet transforms for image coding(IEEE, 1993) Çetin, A. Enis; Gerek, Ö. N.; Ulukuş, Ş.Show more In this paper, a new class of block transforms is presented. These transforms are constructed from subband decomposition filter banks corresponding to regular wavelets. New transforms are compared to the discrete cosine transform (DCT). Image coding schemes that employ the block wavelet transform (BWT) are developed. BWT's can be implemented by fast (O(N log N)) algorithms.Show more Item Open Access An edge-sensing predictor in wavelet lifting structures for lossless image coding(SpringerOpen, 2007) Gerek, Ö. N.; Çetin, A. EnisShow more The introduction of lifting implementations for image wavelet decomposition generated possibilities of several applications and several adaptive decomposition variations. The prediction step of a lifting stage constitutes the interesting part of the decomposition since it aims to reduce the energy of one of the decomposition bands by making predictions using the other decomposition band. In that aspect, more successful predictions yield better efficiency in terms of reduced energy in the lower band. In this work, we present a prediction filter whose prediction domain pixels are selected adaptively according to the local edge characteristics of the image. By judicuously selecting the prediction domain from pixels that are expected to have closer relation to the estimated pixel, the prediction error signal energy is reduced. In order to keep the adaptation rule symmetric for the encoder and the decoder sides, lossless compression applications are examined. Experimental results show that the proposed algorithm provides good compression results. Furthermore, the edge calculation is computationally inexpensive and comparable to the famous Daubechies 5/3 lifting implementation.Show more Item Open Access Equiripple FIR filter design by the FFT algorithm(Institute of Electrical and Electronics Engineers, 1997-03) Çetin, A. Enis; Gerek, Ö. N.; Yardımcı, Y.Show more The fast Fourier transform (FFT) algorithm has been used in a variety of applications in signal and image processing. In this article, a simple procedure for designing finite-extent impulse response (FIR) discrete-time filters using the FFT algorithm is described. The zero-phase (or linear phase) FIR filter design problem is formulated to alternately satisfy the frequency domain constraints on the magnitude response bounds and time domain constraints on the impulse response support. The design scheme is iterative in which each iteration requires two FFT computations. The resultant filter is an equiripple approximation to the desired frequency response. The main advantage of the FFT-based design method is its implementational simplicity and versatility. Furthermore, the way the algorithm works is intuitive and any additional constraint can be incorporated in the iterations, as long as the convexity property of the overall operations is preserved. In one-dimensional cases, the most widely used equiripple FIR filter design algorithm is the Parks-McClellan algorithm (1972). This algorithm is based on linear programming, and it is computationally efficient. However, it cannot be generalized to higher dimensions. Extension of our design method to higher dimensions is straightforward. In this case two multidimensional FFT computations are needed in each iteration.Show more Item Open Access Frequency band characteristics of tree-structured filter banks(The Institution of Engineering and Technology, 1996-04-11) Gerek, Ö. N.; Gürcan, M. N.; Çetin, A. EnisShow more A sub-band decomposition filter bank can be recursively used in a tree structure to divide the frequency domain into various subfrequency bands. The frequency bands of the sub-band signals have a counter intuitive order in such a decomposition. The authors show that the relationship between the frequency content and the index of a sub-band signal can be expressed by an extension of the Gray code.Show more Item Open Access Image denoising using adaptive subband decomposition(IEEE, 2001) Gezici, Sinan; Yılmaz, İsmail; Gerek, Ö. N.; Çetin, A. EnisShow more In this paper, we present a new image denoising method based on adaptive subband decomposition (or adaptive wavelet transform) in which the filter coefficients are updated according to an Least Mean Square (LMS) type algorithm. Adaptive subband decomposition filter banks have the perfect reconstruction property. Since the adaptive filterbank adjusts itself to the changing input environments denoising is more effective compared to fixed filterbanks. Simulation examples are presented.Show more Item Open Access Lossless image compression using an edge adapted lifting predictor(IEEE, 2005-09) Gerek, Ö. N.; Çetin, A .EnisShow more We present a novel and computationally simple prediction stage in a Daubechies 5/3 - like lifting structure for lossless image compression. In the 5/3 wavelet, the prediction filter predicts the value of an odd-indexed polyphase component as the mean of its immediate neighbors belonging to the even-indexed polyphase components. The new edge adaptive predictor, however, predicts according to a local gradient direction estimator of the image. As a result, the prediction domain is allowed to flip + or - 45 degrees with respect to the horizontal or vertical axes in regions with diagonal gradient. We have obtained good compression results with conventional lossless wavelet coders. © 2005 IEEE.Show more Item Open Access Motion-compensated prediction based algorithm for medical image sequence compression(Elsevier BV, 1995-09) Oǧuz, S. H.; Gerek, Ö. N.; Çetin, A. EnisShow more A method for irreversible compression of medical image sequences is described. The method relies on discrete cosine transform and motion-compensated prediction to reduce intra- and inter-frame redundancies in medical image sequences. Simulation examples are presented.Show more Item Open Access Nonlinear subband decomposition structures in GF-(N) arithmetic(Elsevier BV, 1998-01-30) Gürcan, M. N.; Gerek, Ö. N.; Çetin, A. EnisShow more In this paper, perfect reconstruction filter bank structures for GF-(N) fields are developed. The new filter banks are based on the nonlinear subband decomposition and they are especially useful to process binary images such as document and fingerprint images.Show more Item Open Access Polyphase adaptive filter banks for fingerprint image compression(The Institution of Engineering and Technology, 1998-10-01) Gerek, Ö. N.; Çetin, A. EnisShow more A perfect reconstruction polyphase filter bank structure is presented in which the filters adapt to the changing input conditions. The use of such a filter bank leads to higher compression results for images containing sharp edges such as fingerprint images.Show more Item Open Access Subband domain coding of binary textual images for document archiving(Institute of Electrical and Electronics Engineers, 1999-10) Gerek, Ö. N.; Çetin, A. Enis; Tewfik, A. H.; Atalay, V.Show more In this work, a subband domain textual image compression method is developed. The document image is first decomposed into subimages using binary subband decompositions. Next, the character locations in the subbands and the symbol library consisting of the character images are encoded. The method is suitable for keyword search in the compressed data. It is observed that very high compression ratios are obtained with this method. Simulation studies are presented.Show more Item Open Access Vector quantization(Wiley, 2006) Çetin, A. Enis; Gerek, Ö. N.; Akay, M.Show more Vector quantization (VQ) is a critical step in representing signals in digital form for computer processing. It has various uses in signal and image compression and in classification. If the signal samples are quantized separately, the operation is called “scalar quantization.” Consequently, if the samples are grouped to form vectors, their quantization is called “vector quantization.” Changing the quantization dimension from one (for scalar) to multiple (for vectors) has many important mathematical and practical implications. VQ produces indices that represent the vector formed by grouping samples. The output index, which is an integer, has little or no physical relation with the vector it is representing, which is formed by grouping real or complex valued samples. The word “quantization” in VQ comes from the fact that similar vectors are grouped together and represented by the same index. Therefore, many distinct vectors on the multidimensional space are quantized to a single vector that is represented by the index. The number of distinct indices defines the number of quantization levels. Assigning indices to a number of vectors has practical applications in compression and classification. This chapter presents the general layout of the VQ operation, introduces VQ design and optimality conditions, and gives examples about compression and classification applications.Show more